The 33-year-old Morse is hitting .213 with four home runs and 12 RBIs this season.
Tabata, 26, is hitting .289 with four RBIs and a .341 on-base percentage in 27 games. He spent time at Triple A this season and was previously designated for assignment by Pittsburgh in June before heading back to the minors.
The move came before the league's trade deadline at 4 p.m. ET on Friday.
The Dodgers are currently in first place by a half-game in the NL West, while the Pirates are atop the NL Wild Card race.
- Molly Geary